This paper investigates the feasibility of using an energy harvesting device tuned such that its natural frequency coincides with higher harmonics of the input to capture energy from walking or running human motion more efficiently. The paper starts by reviewing the concept of a linear resonant generator for a tonal frequency input and then derives an expression for the power harvested for an input with several harmonics. The amount of power harvested is estimated numerically using measured data from human subjects. Assuming that the input is periodic, the signal is reconstructed using a Fourier series before being used in the simulation. It is found that although the power output depends on the input frequency, the choice of tuning the natural frequency of the device to coincide with a particular higher harmonic is restricted by the amount of damping that is needed to maximize the amount of power harvested, as well as to comply with the size limit of the device. It is also found that it is not feasible to tune the device to match the first few harmonics when the size of the device is small, because a large amount of damping is required to limit the motion of the mass.